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Question

A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of 60. After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30. Find the distance the boat has to travel to reach a point that is exactly above the submarine. [Tan 30=0.57, tan 60=1.73]


A

86.2 m

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B

96.4 m

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C

82.4 m

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D

78.6 m

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Solution

The correct option is A

86.2 m


In the given figure, the person is standing on the boat at A and the submarine moves from B to C.

The boat has to travel distance AD to reach D, a point which is exactly above the submarine.

In ADCtan 30=CDAD0.57=CDADCD=0.57 AD (i)

In ADBtan 60=BDAD1.73=BDADBD=1.73AD(ii)

Now, we can observe that CB=BDCD100=1.73 AD0.57AD100=1.16ADAD=86.2 m

Hence, the boat has to travel 86.2 m to reach a point which is exactly above the submarine.


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